Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <vector>
#include <algorithm>
#include <cstdio>
using namespace std;

int main(){
	int n;
	scanf("%d",&n);
	vector<int>a(n);
	for(int i=0;i<n;i++)scanf("%d",&a[i]);
	sort(a.begin(),a.end());
	reverse(a.begin(),a.end());
	vector<vector<int>>v={
		{2,3,0,1},{0,3,1,2}
	};
	for(int i=3;i<n;i++)v.push_back({0,1,i-1,i});
	vector<double>r;
	transform(v.begin(),v.end(),back_inserter(r),[&a](const vector<int> &e)->double{
		return (a[e[0]]+a[e[1]])*1.0/(a[e[2]]-a[e[3]]);
	});
	printf("%f\n",*max_element(r.begin(),r.end()));
}